Wadcutters are always going to be an issue, and a "sloppy" speedloader, like the HKS, only makes them that much worse.
FMJ "Ball" type bullets will be your best choice, and a somewhat ball, or more conical profile, are usually pretty good as well, and don't have to have a "point" on them to work well.
I mostly use LSWC's with my revolvers, and I use them with my speedloaders, both the Safariland and HKS, and don't usually have any issues (the HKS can be a bit "fiddly" sometimes because of how they are). Even with the sharp, wadcutter edge, the "cone" on top of the wadcutter gets them quickly oriented into the chambers, and they pretty much go right in.
I agree with John, the Safariland Comp II's are the better choice if you have the choice. They keep the rounds fixed in place, with very little movement, and the release is more natural. They don't have the slop in the rounds that the HKS loaders have, and you push down on the loader to release the rounds. Unfortunately, they are limited in what they offer.